Surface of Revolution

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surface of revolution

[¦sər·fəs əv ‚rev·ə′lü·shən]
A surface realized by rotating a planar curve about some axis in its plane.

Surface of Revolution


a surface that can be generated by revolving a plane curve about a straight line, called the axis of the surface of revolution, lying in the plane of the curve. An example of such a surface is the sphere, which may be considered as the surface generated when a semicircle is revolved about its diameter. The curves formed by the intersection of a surface of revolution with planes passing through the axis are called meridians, and the curves of intersection of a surface of revolution with planes perpendicular to the axis are called parallels. If the z-axis of a rectangular system of coordinates x, y, and z is directed along the axis of a surface of revolution, then the parametric equations of the surface of revolution can be written

x = f(u] cos v y = f {u} sin v z = u

where f(u) is a function that determines the shape of the meridian and v is the angle of rotation of the plane of the meridian.